Buttercups (Ranunculus spp.) can be quite invasive, and unfortunately there's not a good selective solution for eliminating them once established. You can spray with a non-selective herbicide such as glyphosate (Roundup), but it may require repeat applications, and will kill other herbaceous plants growing in the same area. Smothering it out by covering it with black plastic is another, non-chemical option, but that, too will kill other herbaceous plants nearby. The key to eradicating buttercups is persistence and thoroughness.